An unknotting result for complete minimal surfaces in \(\mathbb{R}^ 3\)
The main theorem describes the closed connected complementary components of a complete properly embedded minimal surface in 3-space. They are either metrically \(\mathbb{R}^ 2\times[0,h]\) or, up to diffeomorphism, made from an at most countable collection of specified building blocks with a proper collection of handles attached. The proof uses the plane theorem of do Carmo, Peng and Fischer-Colbrie/Schoen and topological methods developed by Meeks, Yau and others.
scientific article; zbMATH DE number 126370
scientific article